If people know about Cesare, they probably know about his father, Rodrigo Borgia, eventual Pope Alexander VI. He gets just as bad a rap in history as Cesare does, both fairly and unfairly. Canon does delve into Cesare's family a bit, with most of the attention going to Lucrezia and Rodrigo. They both have short chapters focusing on them, and Rodrigo is occasionally mentioned to or by Cesare as well. I have some time right now so I'm just going to quickly point out what Cesare's relationship with his father is and how it compares to other trains of thought on it.
This page kind of sums up a very general idea of the father/son dynamic. Thirty chapters in, this is the only time Cesare gives such an automatically nervous reaction (...without the threat of immediate violence). Rodrigo is the head of the family in name and in reality and Cesare is not in a position to challenge that. Even though Rodrigo is many miles away and the threat made was (initially, at least) empty--and even though the man making it is considered a possible danger to the family and therefore not to be trusted--Cesare still jumps at the suggestion.
Rodrigo can be very indulging and will bend over backwards to spoil his children, especially Lucrezia, rotten. According to most reports, however, Cesare was treated somewhat differently from Juan and Lucrezia (not even going to get into Jofre or his half-siblings). I have seen it said that he was favored because he was given more responsibility, that he cowed Rodrigo into submission because he was himself the devil incarnate, that he was detested or at least held at a distance because he was not Rodrigo's son after all... The way the manga seems to be going and the way that I personally prefer to look at it is that Cesare was not indulged the same as his younger brother and sister because of his personality and because of his ability. He was the oldest of this particular batch of children and as such was expected to take on certain responsibilities while his younger siblings were still being coddled. He was also by all accounts more talented than Juan and Rodrigo made full use of his abilities. Cesare was the protege and as such was given a more rigorous education than Juan. Because he did have one older half-brother, it was decided at an early age that he would be the son to follow his father into the ranks of the church. This lent itself to a very different sort of dynamic than the one between Rodrigo and Juan, who was trained instead to be a young noble and who was generally given more leeway.
Rodrigo was clearly very proud of his children. He boasted of their accomplishments and he very openly acknowledged them and made no attempt as pope to hide them or their roles as his support. Lucrezia was even left in charge in the Vatican for a period of time while he was away. Rodrigo's main goal in Italy seems to have been to create a dynastic state for his family in much the same way that other important families had. The difficulty was how to carve out a territory, which led to first Juan and then Cesare being made gonfaloniere. Cesare in canon is aware of his father's pride and of how he lets himself be manipulated by Lucrezia and Juan. I doubt Cesare would be able to manipulate Rodrigo using the same tactics--if nothing else, he is himself far too proud to stoop to them. Their relationship once Cesare became an adult has been described as business-like. I think that is probably putting too strong a head on it. The writings between them that I have seen still seem to show a certain deference to Rodrigo as the father, even as Cesare makes his own moves and argues his own points.
On that note, I doubt Rodrigo was cowed by Cesare. He was a talented politician and he would have known that his son depended on him for his position and holdings--as much as he may have wanted territory for his family, his own position as pope did not depend on it. The balance of power was still clearly in his favor, although that may have changed had things gone on longer. Similarly, I doubt accusations that Cesare was not Rodrigo's natural son. This is not so much because I don't think it could possible be the case as much as I have not seen an argument made for it that I felt was based on solid ground. For the purposes of Camp, at least, Rodrigo is Cesare's biological father.
Cesare in Camp is a teenager and he respects and fears and is feeling rebellious towards his father. As I mentioned before, family is of the utmost importance to him because their position as simultaneously visible and vulnerable in Italy. Rodrigo is a very capable man and in many ways he and Cesare are very similar. They both have the same sort of drive for power and the same sort of cunning. I read once that the reason Cesare was so highly trusted by Rodrigo while Juan was so highly fawned over was because Cesare was simply too similar to his father. He was set on a very similar path to Rodrigo's at a very early age and was held to exceedingly high standards. In canon he is shown to question his father... although not, of course, to his face.
This all makes it so that Rodrigo is someone who Cesare would not like to have in Camp. Even with the knowledge that it is very unlikely that Rodrigo would ever show up (or ever find out what he's been getting up to), he is rather nervous at the thought. Not all of the things he is doing here (although he can justify them all to himself) are things his father would really approve of.